As an example of using a negative training sample, a previous study (Ji et al., 2020) learned graph representations with global structure knowledge in a heterogeneous network consisting of the known associations among miRNA, disease, drug, and protein. Integrating these embeddings with miRNA sequences, disease semantic similarities and so on, a classifier based on Random Forest was applied to discover underlying relationships between miRNAs and diseases.

Meanwhile, more and more approaches preferred to predict unknown miRNA-disease associations only with known ones, so researchers utilized verified associations, such as miRNA-disease, miRNA-gene, and weighted gene-gene, to construct a regularized framework for inferring the latent miRNA-disease associations (Peng et al., 2017a). Similarly, using the identified disease-associated miRNA information, (Luo et al., 2018) built a semi-supervised classifier to calculate the probability of a miRNA related to a given disease, and also utilized graph regularization to avoid overfitting. Considering the sparsity of known data, have also (Luo et al., 2016) proposed a transductive learning-based collective prediction method in which the relevance score was calculated and updated via the disease-miRNA network.

To adequately discover disease-related candidate miRNAs, in (Ding et al., 2018) for example, a heterogeneous disease-gene- miRNA network consisting of three types of nodes and five types of links was built to predict associations via a regression-based model. For fully utilizing verified miRNA-disease associations. In (Pan et al., 2019), the miRNA-disease associations were synchronously predicted and updated via a multi-label, graph-based model, which firstly introduced a set of kernel matrices and then adaptively obtained two optimal kernel matrices. Considering the inherent noise in current databases, a study in (Liang et al., 2019) adaptively learned an affinity graph from various similarity profiles and simultaneously updated the prediction via multi-label learning. According to the latest version of HMDD, a study in (Liang et al., 2018) obtained the semantic similarities of disease and function similarities of miRNA. Then, the similarity matrices and association matrix were iteratively updated to generate the optimized association outcome.

Matrix factorization, a method of multiplying two different entities to generate potential features, is another essential method for predicting miRNA disease associations. As in (Peng et al., 2017b) for example, a matrix recovery approach was utilized to integrate the weight matrix to recover association matrix; hence novel latent associations were accurately inferred without the need for negative samples. Integrated with the label propagation algorithm, a study in (Peng et al., 2022) adopted robust nonnegative matrix factorization to predict underlying associations more precisely. To be specific, using the integrated similarity information, the original adjacency matrix was updated via matrix multiplication to reduce the influence of negative samples. For sparse existing associations and new diseases or miRNAs, a previous work (Xiao et al., 2018) developed a preprocessing step that built the interaction score profiles to facilitate prediction, and then utilized graph regularized non-negative matrix factorization based on integrated multisource data to discover underlying associations.

Although most methods in silico currently focus on discovering unknown miRNA-disease associations, there are some approaches that could identify the multiple relationship types among various associations as the roles miRNAs played in diseases significantly diverged. For example, the down-regulation of mir-16 and mir-15 could induce chronic lymphocytic leukemia in B cell (Calin et al., 2002), while the different expression of serum miRNAs, such as mir-1307-3p, mir-1246 and so on, could assist researchers in tracing breast cancer early (Shimomura et al., 2016). To this end, a more recent study (Huang et al., 2021) innovatively constructed a tensor composed of miRNA-disease-type triples, and then adopted tensor decomposition that utilized the similarity information as decomposition constraints to detect multi-type of miRNA-disease associations. Another study built a novel model for miRNA-disease-type associations by applying tensor robust principal component analysis (Yu et al., 2021a).

Currently, many prediction methods extracted feature embeddings as the input of convolutional neural networks (CNN). Xuan et al. (2018) constructed a dual convolutional neural network, which was divided into the left and right part, to detect underlying associations. The left CNN learned the integrated feature embedding of original information to produce an association score, and the right learned the feature embedding of the network topology to generate the other score. On this basis, a work in (Xuan et al., 2019) firstly projected nodes of miRNAs and diseases into a low dimensional space to obtain feature embeddings, and then utilized network representation learning and two CNN to discover latent disease-associated miRNAs. In (Peng et al., 2019), the low dimensional feature embeddings were selected by an auto-encoder from a three-layer network consisting of multisource data. Then, the association score was calculated by a deep CNN structure, including the fully-connected layer, max-pooling layer, and convolutional layer.

Besides, some Graph Convolutional Network (GCN) based end-to-end models were also implemented to capture candidate associations. In 2020, a work (Li et al., 2020) respectively learned underlying feature embeddings derived from the miRNA function similarity network and the disease semantic similarity network with GCN encoders. Then an association matrix completion was generated from a novel neural inductive model that adopted learned embeddings as input. As in (Chu et al., 2021), a miRNA-disease pair was regarded as a node in homogeneous graphs, which were easier to learn. Then based on graph sampling, the modified GCN algorithm was implemented on the topology and feature graph to cluster similar nodes. Meanwhile, some other graph neural network methods were also employed in this regard. A graph attention network-based method (Li et al., 2022) aggregated different neighbor information with varying weights to obtain the non-linear features of miRNAs and diseases. Combined with the linear features constructed by correlation profiles, latent miRNA-disease associations were inferred via the random forest algorithm. In 2021, Li et al. (2021a) developed an end-to-end framework based on a novel graph auto-encoder model to discover unknown associations. This model aggregated nodes’ neighborhood information via a graph neural network-based encoder, which consisted of the multi-layer perceptron and aggregator function, to obtain low dimensional embeddings and effectively integrate heterogeneous information.

Some methods aimed at predicting type instead of taking association prediction as a binary task. In (Huang et al., 2021) for example, miRNA-type- disease triples were innovatively regarded as a tensor, and then tensor decomposition with relation constraints was implemented to complete the type prediction task. Similarly, a more recent work (Yu et al., 2022) could identify dysregulation, downregulation, or upregulation relationship between miRNA and disease because a depth graph representation learning model was trained based on a knowledge graph constructed by extracting disease-miRNA-type triples from existing databases and numerous experimental data.

To fully understand the synergistic effect of miRNA-miRNA pairs on the pathogenesis of complicated diseases, a study (Luo et al., 2021) proposed a new tensor decomposition model based on a graph attention network to discover potential miRNA-miRNA pairs related to diseases. The graph attention network aggregated the feature embeddings from the miRNA function similarity graph, disease semantic similarity graph, and miRNA sequence similarity graph. With the aggregated feature embeddings, the deep tensor factorization was implemented to reconstruct the association tensor consisting of miRNA-miRNA-disease triples.

Some machine learning methods focused on constructing novel feature engineering with varied features. A random forest prediction model (Wang et al., 2019) adopted similarities of miRNAs and small molecules as features to accurately predict associations. Specifically for cancer, (Li et al., 2021b) innovatively concatenated features extracted from small molecule structures, miRNA sequences, and cancer symptoms to obtain a new feature vector. Then a random forest model was utilized to predict latent cancer-miRNA-small molecule associations. Similarly, Jamal et al. (2012) developed a prediction model by utilizing Naïve Bayes and Random Forest. In 2017, a work (Xie et al., 2017) was proposed to discover the influential miRNA on the drug via the support vector machine, in which feature vectors were drug-miRNA pairs extracted from the related literature.

There are some methods based on random walk algorithm to identify latent miRNA-small molecule associations. In (Liu et al., 2020) for example, Random Walk was utilized in a triple-layer heterogeneous network of disease-miRNA-small molecule association after computing similarities and selecting negative samples. Similarly, a restart algorithm-based Random Walk (Lv et al., 2015) was implemented in a comprehensive network, in which miRNA-miRNA associations, small molecule interactions, and verified miRNA-small molecule targeting pairs were integrated. Meanwhile, some other methods are based on regression algorithm. In Chen et al. (2021) for example, a matrix was defined to represent a heterogeneous network consisting of small molecule similarity, miRNA similarity, and verified miRNA-small molecule associations. Then, the model of the Alternating Direction Method of Multipliers was designed to minimize the nuclear norm of the matrix and obtain predicted scores of underlying miRNA-small molecule associations. Likewise, a work (Wang et al., 2022) developed a prediction model based on the Ensemble of Kernel Ridge Regression. They integrated feature dimensionality reduction with ensemble learning to discover latent small molecule-microRNA associations.

It can be seen in various studies that many computational models adopted matrix factorization. In Yin et al. (2019) for example, a sparse learning method (SLM) was proposed to eliminate noises and improve performance. After the small molecule-miRNA adjacency matrix was decomposed by SLM, latent miRNA-small molecule associations would be obtained via a heterogeneous graph that integrated the similarities of miRNAs and small molecules with the improved association information. At the same time, Wang and Chen (2019) not only adopted similarities of small molecules, miRNAs, and diseases but also integrated with associations between miRNAs and diseases/small molecule. Therefore, a three-layer network was built to obtain potential representations of small molecule-miRNA association via in-layer similarities and cross-layer associations. Then cross-layer dependency inference on the three-layer network was utilized to identify unknown miRNA-small molecule associations. In addition, the model adopted a regularized optimization to avoid overfitting. Afterward, a study (Zhao et al., 2020) applied matrix decomposition in integrated similarity matrixes and obtained small molecule-miRNA pair similarity by calculating the Kronecker product. Additionally, regularized least square method was applied to acquire the mapping relationships between associated probabilities and miRNA-small molecule pairs. Considering the functional similarity of two miRNAs, clinical similarity and chemical similarity of small molecules, a work (Luo et al., 2020) adopted a nonnegative matrix decomposition method for discovering the potential miRNA-small molecule associations. Besides, combining small molecule-disease associations with miRNA-disease associations, Shen et al. (2020a) adopted graph regularization techniques and the iterative approach in a heterogeneous network to obtain the prediction scores of miRNA-small molecule pairs. In Shen et al. (2020b), the prediction performance was improved by a Restricted Boltzmann Machine-based joint learning framework, which integrated miRNA sequence, heterogeneous network knowledge, and small molecule structure data.

Currently, Graph Convolution Network is commonly used to process node classification tasks in the homogeneous network. In Huang et al. (2020) for example, a three-layer latent factor model based on graph convolution was developed to discover unknown miRNA-drug resistance associations. In this end-to-end learning scheme, they could not only utilize high-dimensional attributes but also learn graph embedding features of miRNAs/drugs. To overcome the problem of over-smoothing in conventional graph convolution networks, a work (Yu et al., 2021b) simplified GCN by constructing the embedding propagation layer utilizing a weighted sum aggregator. Then, the ideal representations were obtained by summing over the embeddings in each layer. At last, they applied the inner product to discover the unknown miRNA-drug sensitivity associations. Wang et al. (2021) firstly extracted drug/miRNA representations via a layer attention graph convolution network in the heterogeneous network consisting of known drug similarities, miRNA similarities, and drug-miRNA interactions. Then they obtained the drug/miRNA embedding vectors by concatenating their representations with drug features derived from drug molecular graphs, and the miRNA expression features, respectively. In addition, they utilized compressed tensor network, tensor decomposition, and multi-layer perceptron to extract node-pair embeddings. Eventually, the potential relationship between miRNA and drug resistance was predicted by the completely connected layer with concatenated representations. Similarly focused on prediction for the relationship of miRNA-drug resistance (Zhao et al., 2022), constructed a graph neural network based on positional encoding to extract embeddings from drug molecular graphs and miRNA-drug heterogeneous networks. Then, these embeddings of different layers were combined with a layer attention mechanism to learn powerful feature representations. Finally, the potential miRNA-drug resistance association could be discovered via a multi-channel neural network consisting of tensor network, tensor decomposition, and the multi-layer perceptron.

Besides, there are some other deep learning models based on varied neural networks algorithm. In Deepthi and Jereesh (2021), firstly, the principal component analysis was applied to reduce the dimensions of features extracted from the integrated similarity pairs of drugs and miRNAs. Then, they trained a convolutional neural network to obtain deep retrieved features and adopted the support vector machine classifier to predict latent association. Meanwhile, based on Long Short-Term Memory (LSTM) (Abdelbaky et al., 2021), proposed an encoder-decoder model that could perform on the character level of a sequence. They utilized the LSTM Sequence Auto-Encoders to obtain feature embeddings of miRNAs and small molecules, and sequence-to-sequence learning with an RNN to encode sequences. The input sequence reproduced by the decoder was based on the outcome of the encoder.